I have an epiphyllum plant that has been in my family for 70 years that I know of. My sisters (6) have all gotten their plants to bloom but I can't. I live in Arizona, USA and my plant is thriving otherwise.

This plant is almost certainly E. Oxypetalum by the look of the foliage.
A very popular night blooming 'Species' Epiphyllum that blooms mid summer.
It appears you are growing it as an indoor plant.
In early summer you could apply some bloom booster to encourage flowers.
It seems to be getting good light where you have it. If you are also using artificial light you may be interfering with the plant's natural cycle which may be why it hasn't bloomed.
Try growing it outside, under shade of course.
It looks healthy enough! Good luck with it.

E. Oxypetalum

Steve, I can not agree with you more. It should be outside in a shade area. Mine flowers 4 to 5 times a year from June to October in north California. I have total 80+flowers last year. It is night blooming however it bloomed morning last October due to cool weather.

North California would have a perfect climate for Epi growing Jack.
I have also had Oxypetalum blooms still open on cooler mornings and as it has several flushes of blooms in summer months it's no wonder it is such a widely grown Epi.
Oh and of course it's fragrance is nice too.

I use half strength bloom booster in the early spring when we take the top off the
greenhouse where ours hand during the summer months. I only do this once a year when it's till cool.

I have several different epi cultivars, but most have never bloomed. They are all healthy with lots of foliage, but only HOOKERI STRICTUM blooms. I've had them all for at least 6 years. They are growing outside and get plenty of bright shade and watering. I've had to cut them back every couple of years. My favorite, that used to blooms, was E. Oxypetalum because of the scent and gorgeous flowers. But even she hasn't bloomed in years. Help! What "bloom booster" are you referencing in the previous posts?

There are several different viewpoints on bloom boosters.
Many varieties are sold in garden shops. Basically they are all similar.
They are high in potassium which enhances color and size of blooms but does not necessarily promote actual blooms.
Becky, you say you 'cut back' your plants because they have 'lots of foliage'.
This implies you are using a fertilizer high in nitrogen which promotes growth over blooms.
A low nitrogen fertilizer is advised for Epis.
Epis flower mostly at the ends of their 'branches' so you may have cut off the nodes that would have produced blooms.
Also they bloom better when slightly root bound.
I have no idea what size of container you have yours in.
Hope this helps. 6 years is too long !

Steve - Thanks for the information! I will try to use a fertilizer low in nitrogen. My plants are more root bound than not, as they grow so quickly. To be totally honest, I don't fertilize them hardly at all. I just water them. So maybe I should use a fertilizer that will prompt them to slow growth and produce blooms.